Conformal vacua and entropy in de Sitter space

By R. Bousso, A. Maloney, Andrew Strominger. 2001

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The de Sitter/conformal field theory (dS/CFT) correspondence is illuminated through an analysis of massive scalar field theory in d-dimensional de Sitter space. We consider a one-parameter family of dS-invariant vacua related by Bogolyubov transformations and compute the corresponding Green functions. It is shown that none of these Green functions correspond to the one obtained by analytic continuation from AdS. Among this family of vacua are in (out) vacua which have no incoming (outgoing) particles on ${\mathcal{I}}^{\ensuremath{-}}$ $({\mathcal{I}}^{+}).$ Surprisingly, it is shown that in odd spacetime dimensions the in and out vacua are the same, implying the absence of particle production for this state. The correlators of the boundary CFT, as defined by the dS/CFT correspondence, are shown to depend on the choice of vacuum state---the correlators with all points on ${\mathcal{I}}^{\ensuremath{-}}$ vanish in the in vacuum. For ${\mathrm{dS}}_{3}$ we argue that this bulk vacuum dependence of the correlators is dual to a deformation of the boundary ${\mathrm{CFT}}_{2}$ by a specific marginal operator. It is also shown that Witten's nonstandard de Sitter inner product (slightly modified) reduces to the standard inner product of the boundary field theory. Next we consider a scalar field in the Kerr-${\mathrm{dS}}_{3}$ Euclidean vacuum. A density matrix is constructed by tracing out over modes which are causally inaccessible to a single geodesic observer. This is shown to be a thermal state at the Kerr-${\mathrm{dS}}_{3}$ temperature and angular potential. It is further shown that, assuming Cardy's formula, the microscopic entropy of such a thermal state in the boundary CFT precisely equals the Bekenstein-Hawking value of one-quarter the area of the Kerr-${\mathrm{dS}}_{3}$ horizon.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/01c6547c2ff0da3c5a18e57f9e50729a93f18c5e

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Citations in the corpus

Initial Conditions for Inflation (2002, methodology): “The thermal vacuum lives in a one-complex parameter family of states which are invariant under the isometry group of de Sitter space [17,18,19,20] (see [21] for a recent, clear discussion).”
Holographic Renormalization (2001, background): “Exact solutions for massive scalar fields on de Sitter spacetimes have been recently discussed in this context in [71, 72].”
Static patch solipsism: conformal symmetry of the de Sitter worldline (2011, methodology): “In [25, 27], formulas are derived for matching solutions to the de Sitter wave equation between the future, past, ‘Northern’ and ‘Southern’ diamonds.”
Local bulk operators in AdS/CFT: A holographic description of the black hole interior (2006, background): “As Z ′ → 0 (with other coordinates held fixed) the retarded Green’s function takes the form [24]”
Inflation and de Sitter thermodynamics (2002, background): “Thermal vacuum in the causal patch (“hot tin can”) corresponds to the BunchDavies vacuum of the metric (1) [14,15] and gives a complementary picture of scalar field(s) fluctuations.”
Inflation, holography, and the choice of vacuum in de Sitter space (2002, background): “In this paper we have observed that the vacua discussed in [27] are among the family of de Sitter invariant vacua explored in [52][53].”
Clean Time-Dependent String Backgrounds from Bubble Baths (2002, background): “We do not have a formulation of string perturbation theory which applies to generic time-dependent backgrounds, and we do not have a clear notion of what the observables are in a general background (there being in general no guarantee of the existence of an S-matrix) [1,2].”
Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT (2011, background): “This is of course not a new result, see for example [18, 23].”
Lecture notes on holographic renormalization (2002, methodology): “ using the methods described in this review, one has to address global issues as well. Exact solutions for massive scalar ﬁelds on de Sitter spacetimes have been recently discussed in this context in [72, 74]. Recall that Einstein’s equations in the two cases read (our curvature conventions are give”
CFT Duals for Extreme Black Holes (2008, methodology): “ the Virasoro algebra. In (6.1) we use the Cardy formula in the canonical ensemble, which is easily derived from the more familiar microcanonical version; for a derivation and related discussion, see [26]. In general, the central charge in the Cardy formula is actually an eﬀective central charge c e”